New analytical solution for time fractional Burgers-Huxley equation describing the interaction between reaction mechanisms and diffusion transport

TL;DR

This paper presents a new analytical series solution for the time-fractional Burgers-Huxley equation, demonstrating its convergence and effectiveness through numerical examples in a reproducing kernel Hilbert space.

Contribution

The paper introduces an analytical series solution method for the time-fractional Burgers-Huxley equation and investigates its convergence and numerical validity.

Findings

The series solution converges uniformly to the exact solution.

The proposed method is computationally efficient and effective.

Numerical examples confirm the method's applicability.

Abstract

This manuscript studies the numerical solution of the time-fractional Burgers-Huxley equation in a reproducing kernel Hilbert space. The analytical solution of the equation is obtained in terms of a convergent series with easily computable components. It is observed that the approximate solution uniformly converges to the exact solution for the aforementioned equation. Also, the convergence of the proposed method is investigated. Numerical examples are given to demonstrate the validity and applicability of the presented method. The numerical results indicate that the proposed method is powerful and effective with a small computational overhead.